{
  "id": "1507.03099",
  "version": "v1",
  "published": "2015-07-11T11:45:54.000Z",
  "updated": "2015-07-11T11:45:54.000Z",
  "title": "Explicit Formulas for Partition Pairs and Triples with 3-Cores",
  "authors": [
    "Liuquan Wang"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $A_{3}(n)$ (resp. ${{B}_{3}}(n)$) denote the number of partition pairs (resp. triples) of $n$ where each partition is 3-core. By applying Ramanujan's ${}_{1}\\psi_{1}$ formula and Bailey's ${}_{6}\\psi_{6}$ formula, we find the explicit formulas for $A_{3}(n)$ and $B_{3}(n)$. Using these formulas, we confirm a conjecture of Xia and establish many arithmetic identities satisfied by $A_{3}(n)$ and $B_{3}(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-11T11:45:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P83",
      "05A17"
    ],
    "keywords": [
      "partition pairs",
      "explicit formulas",
      "arithmetic identities",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150703099W"
    }
  }
}